Numerically approximating the second order derivative at the end points of a closed interval

Mathematics Asked by Aulwmate on October 5, 2020

I have approximate the second order derivative of some function $f(x)$ on some interval $[a,b]$. Let $ h =frac{b-a}{n}$ for some positive integer $n$, the discretization of $[a, b]$ will be the following:
x_1 = x_2 +h\
x_2 = x_0 +2h\
x_3 = x_0 +3h\
vdots \
x_n = x_0 +nh = b.

For $i = 2, 3,ldots, n-1$, the second order approximation of $f(x)$ will
f^{”}(x_i) approx frac{f(x_i+h)-2f(x_i)+f(x_i-h)}{h^2}

But if I try to use the same formula to approximate the second order derivative at $x_0$ and $x_n$, I need the values of $f$ at $x_0-h$ and $x_n+h$.

Is there any other way to approximate $f^{”}$ at the end points?

Add your own answers!

Ask a Question

Get help from others!

© 2024 All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP